Two-step inertial method for solving split common null point problem with multiple output sets in Hilbert spaces

Chibueze C. Okeke; Abubakar Adamu; Ratthaprom Promkam; Pongsakorn Sunthrayuth; Chibueze C. Okeke; Abubakar Adamu; Ratthaprom Promkam; Pongsakorn Sunthrayuth

doi:10.3934/math.20231030

AIMS Mathematics

2023, Volume 8, Issue 9: 20201-20222. doi: 10.3934/math.20231030

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Two-step inertial method for solving split common null point problem with multiple output sets in Hilbert spaces

1.
School of Mathematics, University of the Witwatersrand, Johannesburg, South Africa
2.
Operational Research Center in Healthcare, Near East University, Nicosia, TRNC
3.
Mathematics Institute, African University of Science and Technology, Abuja, Nigeria
4.
Department of Mathematics and Computer Science, Faculty of Science and Technology, Rajamangala University of Technology Thanyaburi (RMUTT), Pathumthani, Thailand

Received: 21 May 2023 Accepted: 12 June 2023 Published: 19 June 2023
MSC : 47H09, 47H10, 49J53, 90C25

In this paper, an algorithm with two-step inertial extrapolation and self-adaptive step sizes is proposed to solve the split common null point problem with multiple output sets in Hilbert spaces. Weak convergence analysis are obtained under some easy to verify conditions on the iterative parameters in Hilbert spaces. Preliminary numerical tests are performed to support the theoretical analysis of our proposed algorithm.
- Hilbert space,
- metric projection,
- self-adaptive step size,
- two-step inertial,
- split common null point problem
Citation: Chibueze C. Okeke, Abubakar Adamu, Ratthaprom Promkam, Pongsakorn Sunthrayuth. Two-step inertial method for solving split common null point problem with multiple output sets in Hilbert spaces[J]. AIMS Mathematics, 2023, 8(9): 20201-20222. doi: 10.3934/math.20231030

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Abstract

In this paper, an algorithm with two-step inertial extrapolation and self-adaptive step sizes is proposed to solve the split common null point problem with multiple output sets in Hilbert spaces. Weak convergence analysis are obtained under some easy to verify conditions on the iterative parameters in Hilbert spaces. Preliminary numerical tests are performed to support the theoretical analysis of our proposed algorithm.

References

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